1. You wish to construct   an ideal lowpass filter with

Because the system you build is causal, you actually have

(a)  Find  H(f), and compare   it to the system  function  of the ideal  filter.

(b)   Find the output when the input  is

(c)   Find the error  (difference   between  output  and input)  for the input of part  (b).

 

2. Compare the step response of an RC circuit (output taken across the capacitor) with that of an ideal lowpass filter. Find the value of tift for the ideal filter (in terms of R and  C), which  mini- mizes  the integrated  square  error  between  the two step responses.

3. Design a Butterworth lowpass filter with a 3-dB cutoff at 500 Hz. The roll-off of the filter must be such that the amplitude response is attenuated by at least  50 dB  at a frequency   of 3 kHz.

4.   Design  a spectrum   analyzer   that  can  display   the  magnitude   of  the  Fourier  transform   of the function

 

 

 

 

 

 

 

 

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1. You must choose one of the brands listed below for your presentation o Adidas o Dell o Waterstones 2. Scenario: You have been appointed digital brand consultant for the chosen company and your first task is to present the results of your digital and social media audit to the company’s board: The managing director wants to see your report in advance of the meeting but does not have time for a meeting with you to discuss it. You are therefore required to submit a PowerPoint presentation (created in ‘notes view’) of a maximum 12 slides with accompanying notes explaining your review and totalling no more than 2500 words. Your presentation should contain sufficient notes and images so that it could be fully understood without you being there to explain it. Guidance on content: You should use the topics covered in the weekly lectures to guide you on the contents of your digital communications audit and you should support your critical discussion with evidence of academic reading. You should also make some consideration of the main competitors for the brand and the customer journey. ( important to consider application of factors such as SWOT, porter five forces, Pestle and other market analysis tool that can be used in this scenario). Please bear in mind you must submit notes to accompany your presentation – you should not simply write your report on Powerpoint slides. Slides which contain only text and provide no illustration of the points under analysis are unlikely to score well.

Attachments:

job-card.docx

 

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1.You have been asked to test the disaster recovery plan for a small business in your area.the company has a back up plan that is well documented. 2.Describe the steps you would use to test the plan to ensure that the backup plan would function in case of an actual emergency?

 

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1. You are the CFO of a private college. You know that each student attends school for exactly 4 years. Education is expensive. It costs the school 20k per year per student to run the school, but tuition is only 19k. Effectively, you are losing 1k per student per year. You also know that alumni often give back to the school after graduation. Specifically, on average, students make a 10k donation to the school on their 20th anniversary of graduation. From strictly an NPV point of view, what is the total cash flow, total costs, discounted cash flows, NPV and IRR the school gets on EACH student. The schools discount rate is 6%. Is the school doing ok?

2. The school can either encourage graduates to give more. Specifically, they have an idea that will increase donations from alumni from 10k to 12k. How does this impact the NPV and ROI and the ROI? Is this a good plan?

3. Alternatively, the school can encourage alumni to give earlier. Rather than waiting 20 years, the school believes it can encourage alumni to make a 10k donation 10 years after graduation. How does this impact the key financial measures?

4. Which is the better plan? Ask to give more? Or ask to give earlier?

 

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1. You are asked to determine the market value(mark-to-market) balance sheet for Angus State Bankand loan duration (amounts in $ thousands and duration in years):

Book Value Market Value

Assets Amount Amount Duration

T-bills $ 180 $ 180 0.50

Loans* 5,000 ______ _____

Total Assets 5,180 ______

Liabilities

Deposits 4,184 4,184 0.50

Total Liabilities 4,184 4,184

Equity 996 ______

Total Lia and NW 5,180 ______

*Since this is a simple bank, it has only one type of loan. The loan has a $5,000 book value (current outstanding principal), amortized loan with annual payments, an interest rate of 6.5 percent, and 20-years to maturity. Similar amortized loans today (market interest rate for similar loans) have an interest rate of 7 percent which, is the market yield.

a.Using Excel, determine the market value and duration of the loan and fill in the blanks in the balance sheet above. Please include a copy of your Excel Spreadsheet with your completed exam (you can copy and paste as a picture).

b. What is the average duration of all the assets and what is the average duration of all the liabilities?

Average Duration of Assets: = ______ years

Average Duration of Liabilities:[4,184*0.5]/4184 = 0.50 years

c.What is the leverage-adjustedduration gap? Is Angus State Bank exposed to interest rate risk? Is it exposed if interest rate increase or decrease?

Leverage-adjusted duration gap (DG) = -[DA – kDL]= = ___________ years

The duration gap is _______ years, indicates that an increase in interest rates will lead to an increaseor decrease in net worth. Circle the correct change in net worth

d. What is the forecasted impact on the market value of equity caused by a relative 1.5 percent upward shift in the entire yield curve? [i.e.,Dr/(1+r) = 0.0150]?

The market value of the equity will change by the following:

MVE = -DG * (A) * r/(1 + r) = ______ (_________)(0.015)= $______________.

e.What variables are available to the financial institution to immunize or at least reduce interest rate risk exposure on the balance sheet? Taking one variable at a time, how much would each variable need to change to get DGAP equal to 0?

To immunize the institution for interest rate risk, the Leverage Adjusted DG needs to be zero:

DG = DA–kDL= 0

The choice is to make the duration of assets equal to:

DA= (4184/4987.37)0.50=0.42 years

or the duration of liabilities equal to:

DL= _______________ = ____________ years

Or some combination thereof. Obviously, for any depository institution, this cannon occur, thus the next most cost effect way to reduce interest rate risk is using interest rate swaps.

 

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